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Section: New Results
Stochastic Systems
Simulation-based Verification of HASL (Hybrid Automata Stochastic Logic) Formulas for Stochastic Symmetric Nets
The Hybrid Automata Stochastic Logic (HASL) has been recently defined as a flexible way to express classical performance measures as well as more complex, path-based ones (generically called "HASL formulas"). The considered paths are executions of Generalized Stochastic Petri Nets (GSPN), which are an extension of the basic Petri net formalism to define discrete event stochastic processes. The computation of the HASL formulas for a GSPN model is demanded to the COSMOS tool, that applies simulation techniques to the formula computation. Stochastic Symmetric Nets (SSN) are an high level Petri net formalism, of the colored type, in which tokens can have an identity, and it is well known that colored Petri nets allow one to describe systems in a more compact and parametric form than basic (uncolored) Petri nets. In [27] , we propose to extend HASL and COSMOS to support colors, so that performance formulas for SSN can be easily defined and evaluated. This requires a new definition of the logic, to ensure that colors are taken into account in a correct and useful manner, and a significant extension of the COSMOS tool.
Steady-state control problem for Markov decision processes
We address in (ADD CITATION WHEN IN HAL) a control problem for probabilistic models in the setting of Markov decision processes (MDP). We are interested in the steady-state control problem which asks, given an ergodic MDP M and a distribution , whether there exists a (history-dependent randomized) policy ensuring that the steady-state distribution of M under is exactly . We first show that stationary randomized policies suffice to achieve a given steady-state distribution. Then we infer that the steady-state control problem is decidable for MDP, and can be represented as a linear program which is solvable in PTIME. This decidability result extends to labeled MDP (LMDP) where the objective is a steady-state distribution on labels carried by the states, and we provide a PSPACE algorithm. We also show that a related steady-state language inclusion problem is decidable in EXPTIME for LMDP. Finally, we prove that if we consider MDP under partial observation (POMDP), the steady-state control problem becomes undecidable.